CRII: OAC: A Multi-fidelity Computational Framework for Discovering Governing Equations Under Uncertainty

Northern Arizona University, Flagstaff AZ

Investigators

Abstract

Understanding the nature of physical systems has always been an essential curiosity of humankind, enabling the discovery of many fundamental physical laws governing these systems and processes. Often, in the process, it was seen that a more straightforward explanation is preferred -- embodied in the famous Occam's razor or principle of parsimony. With a similar goal, this project conducts fundamental research seeking to advance the state-of-the-art in understanding the parsimonious principles of physics governing the behavior of a complex physical system under uncertainty. The resulting software framework enables the users to utilize data from a wide range of physical systems to unlock the important aspects of their behavior by analyzing the identified mathematical equations. With this framework, the project investigator provides the community of researchers and educators with a powerful and amenable tool to comprehend and predict the actual behavior of various real-world systems in the presence of uncertainty. Harnessing already developed knowledge in understanding simplified physical systems with similar behavior, the framework builds a novel paradigm using interpretable deep learning for discovering parsimonious governing equations to describe the behavior of complex physical systems under uncertainty. New approaches to utilizing low-fidelity models in defining the system's behavior are also explored, providing even more computationally efficient tools to incorporate prior knowledge. These advancements and the developed software allow the framework to be applied to various application domains. The framework is evaluated with testbed problems such as the behavior of a 20-story building and a benchmark turbulence modeling problem. Furthermore, the resulting framework is applied to other critical problems of complex nature through collaborations, e.g., the spread of wildland fires, enzyme-catalyzed reactions, and the spread of pollutant plumes. The project also emphasizes the importance of identifying parsimonious governing equations to describe the behavior of complex systems through education and outreach activities. Results from the project are submitted to reputable journals and presented at national and international conferences. One graduate student is mentored as part of the project, and findings are incorporated into an undergraduate probability and machine learning course. K-12 outreach efforts led by the project investigator include modules on the discovery of equations, machine learning basics, and using software to infer from data based on the research outputs from this project presented at middle/high school summer workshop programs. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.